Barbara Gordon debuted in Detective Comics #359 (January 1967) as the daughter of Commissioner Jim Gordon, and also the newest addition to Batman's crime-fighting family. Batgirl then gained pop culture icon status when she debuted in the third season premiere of "Batman" on September 14th, 1967. Here, too, she was Commissioner Gordon's daughter. This remained true until the 1985 reboot, Crisis on Infinite Earths, where her origin changed.
Following the reboot, Barbara Gordon is born to Roger and Thelma Gordon, and she is Jim Gordon's niece/adopted daughter in current canon.
Has it ever been explained why this change was made? It seems rather arbitrary, as she still became Commissioner Gordon's adopted daughter.